Computer-aided detection of lung nodules: False positive

Computer-aided detection of lung nodules: False positive reduction usinga 3D gradient field method and 3D ellipsoid fitting

Zhanyu Ge, Berkman Sahiner,a� Heang-Ping Chan, Lubomir M. Hadjiiski,Philip N. Cascade, Naama Bogot, Ella A. Kazerooni, Jun Wei, and Chuan ZhouDepartment of Radiology, The University of Michigan, Ann Arbor, Michigan 48109

�Received 16 November 2004; revised 23 March 2005; accepted for publication 9 May 2005;published 12 July 2005�

We are developing a computer-aided detection system to assist radiologists in the detection of lungnodules on thoracic computed tomography �CT� images. The purpose of this study was to improvethe false-positive �FP� reduction stage of our algorithm by developing features that extract three-dimensional �3D� shape information from volumes of interest identified in the prescreening stage.We formulated 3D gradient field descriptors, and derived 19 gradient field features from theirstatistics. Six ellipsoid features were obtained by computing the lengths and the length ratios of theprincipal axes of an ellipsoid fitted to a segmented object. Both the gradient field features and theellipsoid features were designed to distinguish spherical objects such as lung nodules from elon-gated objects such as vessels. The FP reduction performance in this new 25-dimensional featurespace was compared to the performance in a 19-dimensional space that consisted of featuresextracted using previously developed methods. The performance in the 44-dimensional combinedfeature space was also evaluated. Linear discriminant analysis with stepwise feature selection wasused for classification. The parameters used for feature selection were optimized using the simplexalgorithm. Training and testing were performed using a leave-one-patient-out scheme. The FPreduction performances in different feature spaces were evaluated by using the area Az under thereceiver operating characteristic curve and the number of FPs per CT section at a given sensitivityas accuracy measures. Our data set consisted of 82 CT scans �3551 axial sections� from 56 patientswith section thickness ranging from 1.0 to 2.5 mm. Our prescreening algorithm detected 111 of the116 solid nodules �nodule size: 3.0–30.6 mm� marked by experienced thoracic radiologists. Thetest Az values were 0.95±0.01, 0.88±0.02, and 0.94±0.01 in the new, previous, and combinedfeature spaces, respectively. The number of FPs per section at 80% sensitivity in these three featurespaces were 0.37, 1.61, and 0.34, respectively. The improvement in the test Az with the 25 newfeatures was statistically significant �p�0.0001� compared to that with the previous 19 featuresalone. © 2005 American Association of Physicists in Medicine. �DOI: 10.1118/1.1944667�

Key words: computer-aided detection, false positive reduction, gradient field technique, lung nod-ule detection, ellipsoid fitting

I. INTRODUCTION

Lung cancer is the leading cause of cancer deaths for bothmen and women in the United States. Studies indicate thatpatients treated for stage I lung cancer have better survivalthan patients presenting with more advanced stage disease.1

With the rapid growth of data volumes in computed tomog-raphy �CT� imaging and the potential of applying CT forlung cancer screening, the interpretation of thoracic CT scansis becoming more challenging for radiologists. The challengearises not only because of the increasing amount of data, butalso because of the complex anatomical structures �lungs,soft tissues, vessels, airways� in the thorax. Computer-aideddetection �CAD� systems2–10 can play an important role inmitigating the burden of radiologists by alerting them to sus-picious lesions. Although much effort has been devoted to it,the development of CAD systems for lung nodule detectionon CT scans remains a difficult and ongoing task.

In a lung nodule CAD system, lower threshold values are
usually used during the prescreening stage to achieve high
2443 Med. Phys. 32 „8…, August 2005 0094-2405/2005/32„8

sensitivity at the expense of a large number of false positives�FPs�. The FPs are then analyzed and reduced by featureextraction and classification techniques to increase the speci-ficity. Ideally, the FP reduction stage should eliminate asmany FPs as possible without affecting nodule detection sen-sitivity. A partial summary of the features used for FP reduc-tion can be found in the literature.11 Many of these featuresare variations of standard techniques that are found in theimage processing literature. We are developing feature ex-traction and classification techniques for distinguishing trueand false nodules. Lung nodules vary in shape, size, andlocation within the lungs. Except for spiculated and ill-defined nodules, the shapes of lung nodules that are not at-tached to the pleural surface are mostly spherical, whilethose that are attached to the pleural surface �juxta-pleuralnodules� are hemi-spherical. Pulmonary blood vessels areelongated and more cylindrical. A solitary lung nodule isdefined as a single round intra-parenchymal opacity, at least
moderately well-marginated and less than 3 cm in maximum
2443…/2443/12/$22.50 © 2005 Am. Assoc. Phys. Med.

2444 Ge et al.: False positive reduction in CAD for lung nodules 2444

diameter.12 Many studies have sought to use the shape dif-ference between round nodules and elongated vessels to re-duce FPs in CAD for lung nodule detection.

Armato et al.7,13 used an automated nodule detectionmethod based on two- and three-dimensional ��2D� and�3D�� analysis of CT image data. Lung segmentation wasperformed on a 2D section-by-section basis to construct alung volume. Lung nodule candidates were identified usingmultiple gray-level thresholding of the lung volume, group-ing voxels according to 18-connectivity, and thresholding us-ing a volume criterion. For each of the nodule candidates,they derived 9 features to differentiate true positives fromfalse positives, including circularity, sphericity, and compact-ness. Rule-based and LDA classifiers were used to reducefalse positives. Their method was applied to 43 scans total-ling 1209 axial sections and containing 171 identified nod-ules. The automated method yielded an overall nodule detec-tion sensitivity of 70%, with an average of 1.5 FPs persection. In a more recent study,14 they reported an improvedperformance of 80% sensitivity at 1.0 FPs per section. Ko etal.5 analyzed nodule candidates by location and shape to dif-ferentiate normal structures from nodules. Candidates werecategorized into five regions of the lungs based on locationinformation, and shape information was characterized by cir-cularity of the candidate nodules. The algorithm, tested on 16chest CT scans containing 370 nodules, achieved a sensitiv-ity of 86% at 2.3 FPs per section. Lee et al.6 used a templatematching technique to detect lung nodules on chest CTscans. A genetic algorithm was designed to determine thetarget position and to select a template image from the ref-erence patterns. The four reference templates were estab-lished according to the gray-level values of 3D Gaussiandistributions, with values in the z direction �the vertical di-rection� regulated by a factor. The algorithm worked only onthree slices in the z direction to detect nodules less than 3 cmin diameter. The matching was determined by a referencevolume and the normalized gray-scale correlation of the can-didate region. Thirteen features were extracted to eliminateFPs. They applied their algorithms to 557 axial sections from20 scans, obtaining a sensitivity of 72% at 1.1 FPs per sec-tion. Kanazawa et al.10 developed a rule-based CAD systemusing features such as size, circularity, contrast, convexnessand roundness, and applied it to a data set of 450 chest CTscans containing 230 lung nodules. Their system detected90% of nodules characterized as definitely malignant or sus-picious by three radiologists at 8.6 FPs per scan. The samesystem was later applied to 249 different scans in a field test,detecting 34 of the 47 nodules �72%� characterized as suspi-cious for malignancy by three radiologists, and 10 of the 14nodules �71%� characterized as benign.15 All of the above-discussed studies analyzed the shape information of the ex-tracted nodule candidates to discriminate the lung nodulesfrom normal structures through compactness or circularity ona stack of 2D sections. Li et al.16 proposed three selectiveenhancement filters for dots, lines, and planes, which cansimultaneously enhance objects of a specific shape and sup-press objects of other shapes. They blurred the CT image
with a Gaussian kernel that matched the size of the nodule to
Medical Physics, Vol. 32, No. 8, August 2005

be detected before calculating the eigenvalues of the Hessianmatrix that were used for selective enhancement. They usedmultiple scales of the Gaussian kernel to find a match withthe nodule size. The prescreening algorithm was applied to73 scans and detected 71 of 76 lung nodules with an averageof 4.2 FPs per section. Brown et al.9 used a data set of 14chest CT scans obtained using 1 mm collimation for the de-velopment of a system to detect micronodules �nodules witha diameter of less than or equal to 3 mm�, and tested theirsystem on 15 different scans. They achieved 100% sensitiv-ity for lung nodules larger than 3 mm, and 70% sensitivityfor lung nodules less than or equal to 3 mm at 15 FPs perscan.

The computer-aided detection system developed in ourlaboratory2 consists of the following steps: lung volume seg-mentation, lung partitioning and sectioning, lung nodule can-didate detection and segmentation, volume of interest �VOI�extraction, feature extraction, and feature classification. Werefer to the first three steps as the adaptive prescreeningstage, and the last three steps as the FP reduction stage. The3D gradient field method and the ellipsoid fitting developedin this study are used to extract shape features in the FPreduction stage.

The gradient field information has been used to study thedistribution of intensity fields or shape information of objectsin physics, computer vision, and many other applications.Recent work on image gradient analysis has demonstrated itspotential in different areas of CAD such as breast tumordetection and colonic polyp detection and FP reduction.17

These investigators extracted gradient field information fromindividual 2D images or from a 3D data set and detectedobjects by using the maximum gradient convergence within apredefined range along the radial direction. Our 3D gradientfield method aims at exploiting the shape information of theidentified objects in the 3D image gradient field to distin-guish nodules from other tissues in the lungs, and hencereduce FPs and increase specificity for automated lung nod-ule detection.

Ellipsoid fitting has been used for feature extraction in anumber of applications in medical imaging, visualization,and pattern recognition.18–20 We applied 3D ellipsoid fittingto the binary objects extracted during the prescreening stage,and used the lengths and length ratios of the principal axes asdiscriminant features for classification of spherical and elon-gated objects.

In our previous work, we used 19 features related to theshape of the detected objects and the gray-scale distributionwithin the objects for FP reduction.2 In this study, we ex-tracted a total of 25 new features based on gradient fieldanalysis and ellipsoid fitting for the same purpose. We com-pared the FP reduction performance in the new and previousfeature spaces. Linear discriminant analysis with stepwisefeature selection was used for distinguishing true lung nod-ules from FPs. The classification performance was measuredusing the area Az under the receiver operating characteristic�ROC� curve and the overall detection accuracy was evalu-ated by free-response receiver operating characteristic
�FROC� analysis.


II. METHODS

A. Data sets

The chest CT scans used in this study were collected withapproval from the Institutional Review Board. A total of 91chest CT scans in 63 patients were selected from the patientarchives. The CT scans were randomly selected except fortwo criteria: the slice thickness was 2.5 mm or less and theCT scan contained no more than six lung nodules. The dataset was further separated into a main data set and a second-ary data set. The main data set consisted of 82 chest CTscans from 56 patients with lung nodules, whose lungs werefree of other parenchymal abnormality that focally or dif-fusely increased lung attenuation, such as interstitial or al-veolar disease. The secondary data set consisted of the re-maining 9 chest CT scans from 9 patients that containedareas of visible dependent atelectasis21 in addition to the lungnodules. These cases, referred to as “atelectasis cases” in thefollowing discussion, were separated from the main data setbased on the judgment of experienced thoracic radiologiststhat they contained sufficient dependent atelectasis to createconspicuous ground glass opacity on the CT images. An ex-ample of an axial section from a chest CT case with depen-dent atelectasis is shown in Fig. 1. This axial section containstwo nodules, one of which is a subtle juxta-pleural nodule,and the other is an 8.5 mm internal nodule.

For the chest CT scans in our data set, all 2D image sec-tions had a matrix size of 512�512 pixels. The in-planeresolution ranged from 0.546 to 0.839 mm, with an averageof 0.674 mm. The section thickness ranged from1.0 to 2.5 mm. Many of the scans in our data set only con-tained a partial volume of the lungs. Although the use of fulllung scans is preferable, we decided not to exclude the par-tial scans because it is important to train and test the devel-oped algorithms with as large a data set as possible. Since wewill report the sensitivity for individual nodules and the FPrate as the number of FPs per section, the partial scan shouldprovide similar performance statistics as a full thoracic CTscan. In this study, we used the main data set for training and

FIG. 1. A CT slice containing significant dependent atelectasis in our sec-ondary data set. A subtle juxta-pleural nodule �nodule 2� that was detectedby the CAD program is at the upper chest wall, in addition to the 8.5 mmlobulated nodule �nodule 1� located medial to it.

testing of a classifier in a leave-one-patient-out resampling


scheme. The trained classifier was also applied to the second-ary data set for evaluation of its performance in the atelecta-sis cases and for comparison with that in the main data set.

Three experienced thoracic radiologists read differentsubsets of our CT database using a graphical user interface�GUI� specifically designed in our laboratory for reading theCT scans and collecting data of the nodule characteristics.The GUI was developed in collaboration with the radiolo-gists such that nodule characteristics and their descriptors ofclinical relevance were included. The radiologists marked thelocation of the lung nodules, measured the long and short-axis lengths of the nodules on the slice containing the largestaxial cross section of the nodule using an electronic ruler,and rated the conspicuity of the nodules relative to thoseencountered in clinical practice on a 5-point scale, with 1representing the most obvious and 5 representing the subtlestnodules. The radiologists also rated the nodule margins assmooth, lobulated, or spiculated/irregular, and identified nod-ules that were juxta-pleural or juxta-vascular.

The radiologists marked 116 solid nodules on the 3551sections in the main data set; nodule size ranged from3.0 to 30.6 mm �median=7.8 mm�. The average conspicuityof the nodules was 2.4. Nineteen lung nodules in the maindata set were biopsy-proven malignancy, and 90 were benignby either biopsy or two-year follow-up showing lack ofchange or disappearance of the nodule. For seven nodules inthe main data set, neither biopsy nor two-year follow-up in-formation was available to ascertain the nodule status as ma-

FIG. 2. Distribution of nodule sizes for the main and secondary data sets.

FIG. 3. Distribution of nodule conspicuity �1=Most conspicuous, 5=Least
conspicuous� for the main and secondary data sets.


lignant or benign. In the secondary data set, the radiologistsmarked 17 lung nodules on the 581 sections, of which 4 weremalignant, 10 were benign, and 3 had insufficient informa-tion to ascertain the nodule status. The nodule size rangedfrom 3.9 to 15.6 mm �median=7.8 mm�. The average con-spicuity of the nodules was 3.2. Figures 2–4 show the distri-butions of the nodule size, conspicuity ratings, and marginratings for the main and secondary data sets.

B. 3D gradient field features

A block diagram of our CAD system, which consists ofthe prescreening and FP reduction stages, is illustrated in Fig.5. The prescreening algorithm segmented suspicious objectswithin the lungs based on weighted k-means clustering. Inour previous work, 19 features related to the shape of a de-tected object and gray-scale distribution within the object

FIG. 4. Distribution of nodule margin ratings for the main and secondarydata sets.

FIG. 5. Schematic illustration of our CT lung nodule CAD system.


were extracted for FP reduction. The details of our prescreen-ing algorithm and the definition of these features can befound in the literature.2

The main focuses of this study, extraction of 3D gradientfield features and extraction of 3D ellipsoid features, areshown in boldface in Fig. 5. A block diagram of the 3Dgradient field algorithm is shown in Fig. 6. The 3D gradientfield algorithm used the VOIs extracted after the prescreen-ing stage as its input. Since the identified VOI might notinclude the entire nodule, it was first extended in all direc-tions by a fixed amount �5 mm in this study�. A 3D isotropicinterpolation algorithm was applied to each VOI to generatevoxels with equal side-lengths in all three dimensions. Theinterpolation does not improve the spatial resolution in the zdirection, but the isometric voxels facilitate the implementa-tion of the 3D gradient field calculation and other imageprocessing operations in the CAD system. 3D gradient fieldimage data were obtained by filtering each of the VOIs withthree 3�3�3 convolution kernels, one for each of the x, y,z directions. The kernel for extracting the z-direction gradientis shown in Fig. 7, where the solid disc represents the voxelunder consideration and the circles represent the kernel vox-els. The 3D kernel coefficients were inversely proportional toa power m of the distance between the voxel of interest andthe voxel at a given location on the kernel, which is a gen-eralization of the isotropic 2D kernel suggested by Jain.22

The kernel coefficients for kernel voxels 0 to 17 were deter-

FIG. 6. Schematic illustration of our 3D gradient field analysis algorithm.

mined by


wi =

1

dim

� j=0

8 1

djm

,

�1�di = ��xi − x0�2 + �yi − y0�2 + �zi − z0�2, �i = 0,1, . . . ,8� ,

wi = − wi−9, �i = 9,10, . . . ,17� , �2�

where, di=the distance between the ith kernel voxel�xi ,yi ,zi� and the center voxel �x0 ,y0 ,z0�, and m=power in-dex of the distance, chosen as m=1 in this study. The gradi-ent component in the z direction can be expressed as

Gz = �i=0

17

Viwi, �3�

where, Vi=gray-scale value at kernel voxel i. The gradientcomponents in the x and y directions, Gx and Gy, can becalculated similarly.

The main purpose of the gradient features is to discrimi-nate objects whose gray-level distribution is approximatelyradially symmetric from other objects whose gray-level dis-tribution are highly asymmetric. For example, consider thestandard deviation of the gradient magnitude calculated overpoints on a spherical surface centered at the centroid of twoobjects, of which the first object represents an idealized nod-ule, and the second object approximates a vessel. If the graylevels of the first object are radially symmetric, then the stan-dard deviation of the radial gradients would be zero. Assumethat the second object is derived from the first object byrescaling its axes dramatically so that the second object lookslike a stretched ellipsoid. The standard deviation for the sec-ond object would be substantially different from zero. In thisidealized situation in a continuous space, the standard devia-tions are calculated over all the points on the surface of asphere centered at the centroid of the object. In a 3D CTvolume with discrete voxels, it is desirable to consider alarge number of voxels uniformly distributed over the sur-face of the sphere in order to capture the possible deviation

FIG. 7. 3D gradient kernel for the z-direction gradient calculation. A similarkernel was used for the x direction and y direction by rotating the two planesof nonzero weights to be perpendicular to the x axis and the y axis,respectively.

from symmetry. In this study, taking into consideration the


tradeoff between computation time and adequate sampling,we chose to consider the statistics of the gradients over 26voxels uniformly distributed over a spherical shell. The 26directions would cover all neighboring voxels for a noduleabout 3�3 voxels in size. The sampling became more sparseas the nodule size increased but it would still sample thegradient field in all directions.

To estimate the 3D gradient field vectors at voxels withinthe VOI segmented by our adaptive prescreening algorithm,we first calculated Req, the radius of the equivalent sphere,which has the same volume as the nodule candidate, Vobj,using

Req =�3 0.75Vobj

�= 0.62�3 Vobj. �4�

To calculate the gradient field features at a voxel Cs, threespherical shells of radii Req and Req±�R were drawn cen-tered at the voxel Cs, where �R=radial distance betweenadjacent shells. The use of three shells instead of just oneshell at Req was intended to decrease the effect of the poten-tial error in object volume estimation from the prescreeningstage. The radial distance between adjacent shells was cho-sen as �R=0.20Req in this study so that it was adaptive to thenodule size. On each of the three shells, j=0,1 ,2, we used26 uniformly distributed voxels Pij �i=0,1 ,2 , . . . ,25� tocompute gradient statistics. An example of the ith radial vec-tor, rij, radiating from the center voxel, Cs, to the ith voxelon the jth shell is shown in Fig. 8. The gradient field orien-tation at voxel i on shell j, SDij, was defined as the cosine ofthe angle between the ith radial vector, rij, and the gradientfield vector, gij, as shown in Fig. 8,

SDij =rij . gij

�rij��gij�, i = 0,1,2, . . . ,25, j = 0,1,2, �5�

where the center dot denotes the inner product, and �rij� and�gij� are the magnitudes of the vectors rij and gij, respectively.The gradient field strength, SMij, is the magnitude of gij, i.e.,

SMij = �gij� . �6�

A total of 19 gradient field features were extracted from thestatistics of the �SDij and the �SMij on three shells andalong the 26 radial directions to describe the shape informa-tion within the VOI containing a segmented object. Seven ofthese were extracted from the gradient field strength, and 12

FIG. 8. ith radial vector on the jth spherical shell, and the gradient fieldvector.

were extracted from the gradient field orientation.


Among the seven gradient field strength features, six wereobtained based on shells, and one along the radial direction.The six shell-based gradient field strength features were theaverage �GMav�, standard deviation �GMstd�, coefficient ofvariation �GMcv�, maximum value �GMmax�, minimum value�GMmin�, and the ratio of standard deviation to median value�GMstd/med� of the gradient field strength. To define thesefeatures, we first employed the common definitions of aver-age, standard deviation, etc., on one shell for one voxel in theVOI, and then combined the information from multipleshells and different voxels within the VOI. For example, the�GMstd� feature was defined as

GMstd = minv�Umin

j�J��i=0

K−1�SMij − �i=0

K−1SMij/K�2

K − 1�� ,

�7�

where v=the voxel under consideration; U=a collection ofall the voxels within the VOI; J=a collection of the threeshells centered at v; and K=the number of voxels on theshell that were inside the lung volume, K�26. As mentionedpreviously, for an ideal spherical nodule, the standard devia-tion of the gradient magnitude over the voxels Pij is zero forany j, i.e., any radius. However, for a real nodule, the stan-dard deviation will depend on the radius. To capture the stan-dard deviation for the radius at which the gray-level valuesof the object were most similar to a radially symmetric ob-ject, we first computed the minimum over the three spherical

�GDmed/av�, squared ratio of minimum value to maximum


shells centered at voxel v, as indicated by the inner minimumoperator in Eq. �7�. The outer minimum operator in Eq. �7�took into account the fact that the standard deviation will bezero only if the shells are centered at the centroid of an idealnodule. Since the centroid of the segmented object may notbe the center of symmetry of an idealized object, and sincetrue nodules may not have a center of symmetry at all, wecomputed the minimum over all pixels within the VOI to findthe standard deviation for the voxel that most resembled acenter of symmetry. Similar definitions were used to find theother five gradient field strength features that were based onshells.

In addition to these six gradient field strength features thatwere based on shells, we also defined a radial gradient fieldstrength feature, GMRstd/av, along the radial direction. As im-plied by the subscript �std/av�, the GMRstd/av feature con-tained two components, the average and the standard devia-tion of the gradient magnitude. Each of the 26 voxels �Pij,i=0,1 ,2 , . . . ,25� on the surface of the jth shell defines aradial direction away from the center of the sphere. For thisradial feature, the average was defined by first finding themaximum gradient magnitude in each radial direction amongthe shells, and then computing the mean over the 26 direc-tions. Similarly, the definition of the standard deviation in-volved the maximum gradient magnitude in each radial di-rection among the shells. This radial feature was thereforedefined as

GMRstd/av = minv�U� 1

�i=0

K−1maxj�J

�SMij��i=0

K−1�K · max

j�J�SMij − �i=0

K−1maxj�J

�SMij�2

K − 1 . �8�

Twelve gradient field orientation features were defined,based on �SDij on the shells or in the radial directions. Twogradient field orientation features obtained in the radial di-rections were average maximum gradient field orientationvalue �GDRav�, and standard deviation of the maximum gra-dient field orientation value �GDRstd�. Similar to the radialgradient field strength features, these radial gradient field ori-entation features were defined by first finding the maximumgradient field orientation in each radial direction among theshells, and then computing the appropriate statistics. Theother ten gradient field orientation features were derivedfrom �SDij based on shells. They were the maximum value�GDmax�, minimum value �GDmin�, median value �GDmed�,average �GDav�, standard deviation �GDstd�, coefficient ofvariation �GDcv�, ratio of standard deviation to median value�GDstd/med�, ratio of median value to average value

value �GD�min/max�2 �, and squared ratio of median value to

maximum value �GD�med/max�2 � of the gradient field orienta-

tion feature. To compute these ten features, we first com-puted the appropriate statistics, e.g., maximum, minimum,median, average, etc., over each shell, and then combined theinformation from different shells and different voxels withinthe VOI. The definitions of these features were very similarto those of the corresponding gradient field strength featuresdescribed earlier, except that SMij was replaced by SDij. Forexample, the standard deviation �SDstd� feature was definedas

GDstd = minv�Umin

j�J��i=0

K−1�SDij − �i=0

K−1SDij/K�2

K − 1��

�9�


C. 3D ellipsoid features

3D ellipsoid fitting has been widely used to approximatethe shape or distribution of a set of data points. There arenine parameters for an ellipsoid, three for the center coordi-nates, three for the lengths of the principal axes, and three forthe orientations of the axes. In this application, we are onlyinterested in the lengths of the three principal axes, fromwhich features are derived to characterize the shapes of theidentified objects. Let q1, q2, and q3 denote the lengths of theprincipal axes of the ellipsoid fitted to an object segmentedin the prescreening stage of our algorithm. The six ellipsoidfeatures were defined as

L11 = q1, L22 = q2, L33 = q3, L12 =q1

q2,

�10�

L13 =q1

q3, L23 =

q2

q3.

For spherical nodules, the values of L12, L13, and L23 areclose to unity, while for elongated objects such as vessels,one of the ellipsoid axes will be much longer than the othertwo. Assuming q1 is the longest axis and q3 the shortest, L13

will be much larger than 1. These features can thus helpdifferentiate nodules from vessels.

D. Feature spaces

As discussed at the beginning of Sec. II B, we had previ-ously developed 19 features for FP reduction.2 These featureswere object volume, surface area, average and standard de-viation of the gray-scale values, bounding box and its vol-ume, ratio of object volume to bounding box volume, maxi-mum 2D area, maximum perimeter, maximum circularity,maximum eccentricity, maximum fitting ellipse major andminor axes and their ratio, compactness, and skewness, andkurtosis of the gray-level histogram. To measure the effect ofthe new features developed in this study on the detectionperformance, we performed ROC and FROC analyses inthree feature spaces. The first feature space contained the 25new features �19 gradient field and 6 ellipsoid features�,which is referred to as the new feature space. The secondfeature space included the previous 19 features, and is re-ferred to as the previous feature space. The third featurespace combined the 19 previous features and the 25 newfeatures. This feature space, which contains 44 features, isreferred to as the combined feature space.

E. Classification

In this study, we used a linear discriminant analysis�LDA� classifier with stepwise feature selection to discrimi-nate between true and false positives. In stepwise featureselection, individual features are entered into or removedfrom the selected feature pool by analyzing the effect of theentry or removal on a selection criterion. Given a set offeatures already in the selected feature pool, the stepwiseprocedure inspects the significance of the change in the se-
lection criterion that would be obtained by entering each

feature that has not been selected into the feature pool one ata time. The best feature at a given step is entered into theselected feature pool if the significance of the change ishigher than a pre-selected F-to-enter threshold, Fin. Anotherthreshold, Fout, is preselected for feature removal. The toler-ance of entering a feature that has a high correlation with thefeatures that are already in the selected feature pool is set byusing a third threshold tol. For a given training data set, thethresholds Fin, Fout, and tol need to be optimized to yield anoptimal or near-optimal set of features. We used a simplexalgorithm23,24 to perform the optimization, which minimizesan error function through rolling the defined hyper-polygontoward the direction of the vertex with the minimum errorvalue. The optimization is terminated when the improvementin the error function stagnates or when the number of itera-tions reaches a preset value.

Training and testing for the main data set were performedusing a leave-one-patient-out scheme. The main data set of56 patients was partitioned 56 times into 55 training casesand one test case by changing the test case in a round-robinmanner. For each partition, feature selection with simplexoptimization and LDA coefficient estimation were performedbased on the CT scans of the training cases, and the designedclassifier was applied to the CT scans of the left-out test case.The test scores obtained by this leave-one-patient-out parti-tioning method were used as the decision variable in theROC and FROC analyses. The ROC curves were estimated

FIG. 9. Example of identified TP and FP objects and the spatial distributionof their average gradient field orientation that has been mapped linearly to agray scale of 256. The feature, GDav, was calculated in the 3D volume of
interest. These examples show the central slice through each of the VOIs.


using the LABROC software by Metz et al.,25 which also pro-vides the area Az under the curve and its standard deviation.To obtain the test results for the secondary data set, the FPclassifier was trained using the entire main data set, and thenapplied to the CT scans of the secondary data set.

III. RESULTS

Figure 9 shows examples of the central slice through theVOIs containing objects identified after prescreening. Thecorresponding average gradient field orientation at everypixel on the slice, and the values of the GDav feature withinthe VOIs are also shown to illustrate the gradient field ori-entation of and around the objects.

A. Main data set

For the main data set, our prescreening stage detected24 563 nodule candidates in the 82 chest CT scans, including111 true positives and 24 452 FPs. The sensitivity of theprescreening algorithm was 96% �111/116� and the numberof FPs per section was 6.92. Of the five lung nodules thatwere not detected at this stage, four were connected to fis-sures, and one was connected to blood vessels.

In the new feature space, the stepwise feature selectionalgorithm selected an average of 13.7 features using the

FIG. 10. Test ROC curves in different feature spaces for the main data set.The Az values are 0.88±0.02, 0.95±0.01, and 0.94±0.01 for the previous,new, and combined feature space, respectively. The differences in the Az

values between the new and the previous feature spaces and between thecombined and the previous feature spaces were both statistically significantwith a two-tailed p-value�0.0001. The difference between the new and thecombined feature spaces did not achieve statistical significance.

FIG. 11. Test FROC curves in different feature spaces for the main data set.


simplex-optimized feature selection parameters. The test Az

of the LDA classifier was 0.95±0.01 with 0.37 FPs/section at80% sensitivity, as shown in Figs. 10 and 11. In the previousfeature space, stepwise feature selection selected an averageof 9.4 features. The test Az was 0.88±0.02 with 1.61 FPs/section at 80% sensitivity. In the combined feature space, theaverage number of selected features was 24.4, and the test Az

was 0.94±0.01. At 80% sensitivity there were 0.34 FPs/section. The test results are summarized in Table I. The dif-ference in the Az values between the new and the previousfeature spaces was statistically significant �two-tailed p-value�0.0001�. Likewise, the difference in the Az valuesbetween the combined and the previous feature spaces wasstatistically significant �two-tailed p-value�0.0001�. Thedifference between the new and the combined feature spacesdid not achieve statistical significance.

The characteristics of the false negative �FN� nodules inthe main data set at a decision threshold of 0.5 FPs/section inthe three feature spaces are tabulated in Table II. In the 82chest CT scans, 27 nodules were rated as spiculated/irregular,36 nodules as juxta-pleural, and 8 nodules as juxta-vascularby the radiologists. At 0.5 FPs/section, there were 38 FNs inthe previous space �including 9 spiculated nodules, 12 juxta-pleural nodules, 5 juxta-vascular nodules�. The number ofFNs was reduced to 14 in the new feature space �including 4spiculated nodules, 8 juxta-pleural nodules, and 1 juxta-vascular nodule�, and 15 in the combined feature space �in-cluding 7 spiculated nodules, 7 juxta-pleural nodules, and 1juxta-vascular nodule�. The drastic reduction in the FNs, es-pecially for the more regularly shaped �near spherical� nod-ules, in the new and combined feature spaces indicated theeffectiveness of the new features in distinguishing true nod-ules and false positive objects.

TABLE I. Test Az values and the FP rate in the different feature spaces for themain data set.

Feature space Az valueFPs/section

at 80% sensitivity

New feature space 0.95±0.01 0.37Previous feature space 0.88±0.02 1.61Combined feature space 0.94±0.01 0.34

TABLE II. Characteristics of the false negative �FN� nodules for the maindata set at a FP rate of 0.5/section in the different feature spaces.

Nodule types

Totalidentified byradiologists

Previousfeaturespace

Newfeature space

Combinedfeature space

Spiculated/irregular 27 9 4 7Juxta-pleural 36 12 8 7Juxta-vascular 8 5 1 1Other 45 12 1 0Total No. of FNs at0.5 FPs/section

38 14 15


B. Secondary data set

For the secondary data set of 9 chest CT scans with de-pendent atelectasis, the prescreening algorithm detected 5592nodule candidates, including 16 of the 17 true nodules and5576 FP objects. The number of FPs/section was 9.59�5576/581�, much larger than that for the main data set. Thetest results are presented in Figs. 12 and 13, and Table III.The number of FPs/section at 80% sensitivity for this groupwas higher than that in the main data set because of theatelectasis opacities on the CT images. There were a largenumber of small structures with compact shapes in these ar-eas, as shown in Fig. 14, compared to the main data set.Many of these structures could not be eliminated in the FPreduction stage and resulted in a large number of FPs for thesecondary data set. The Az values in the previous, new, andcombined feature spaces were 0.75±0.07, 0.86±0.05, and0.88±0.05, respectively. The difference in the Az values be-tween the combined and the previous feature spaces was sta-tistically significant �two-tailed p-value=0.05�. The differ-ence between the new and the previous feature spaces did notachieve statistical significance.

FIG. 12. Test ROC curves in different feature spaces for the secondary dataset that consisted of cases containing significant atelectasis. The Az valuesare 0.75±0.07, 0.86±0.05, and 0.88±0.05 for the previous, new, and com-bined feature space, respectively. The difference in the Az values betweenthe combined and the previous feature spaces was statistically significant�two-tailed p-value=0.05�. The difference between the new and the previousfeature spaces did not achieve statistical significance

FIG. 13. Test FROC curves in different feature spaces for the secondary data
set that consisted of cases containing significant atelectasis.

IV. DISCUSSION

Figure 9 shows examples of the spatial distribution of theaverage gradient field orientation for nodules and vessels.The gradient field orientation value was calculated in the 3Dvolume of interest and the examples show only the centralslice through the VOI. The average gradient field orientationfeature within the VOI, GDav, can distinguish the vessel fromthe circumscribed and juxta-pleural nodules, and one of thespiculated nodules in these examples. Through a statisticalanalysis of all the gradient field orientation and gradient fieldstrength features, the shape information of the candidate ob-jects can be explored in a more thorough way. For spiculatednodules, the gradient field features may not be able to pro-vide as high a level of discrimination from the vessels be-cause the gradient direction around the spicules may not beradial. Gradient field features depend on the distribution ofthe gray-level values around the candidate objects. As a re-sult, they are less influenced by the accuracy of the segmen-tation because the shape information is derived from theoriginal gray-scale image data, not the segmented binary im-age data. Ellipsoid features represent the shape informationin a different manner. They characterize the outline of thesegmented objects, which is highly dependent upon the ac-curacy of object segmentation. The combination of the gra-dient field and the ellipsoid features provides a more detaileddepiction of the objects by utilizing both types of informa-tion.

Our test results indicate that compared with our previ-ously designed features, the newly designed gradient fieldand ellipsoid features significantly improved the FP reduc-tion performance. Table I shows the improvement in perfor-mance of the LDA classifiers designed with the 25 new fea-

TABLE III. Test Az values and the FP rate in the different feature spaces forthe secondary data set.

Feature space Az valueFPs/section

at 80% sensitivity

New feature space 0.86±0.05 2.28Previous feature space 0.75±0.07 6.32Combined feature space 0.88±0.05 2.15

FIG. 14. Nodule candidates detected in the prescreening stage for the case
with significant dependent atelectasis shown in Fig. 1.


tures over that with the previous 19 features alone. The testAz value is significantly improved �p�0.0001� from 0.88 to0.95 with the use of the new features. The number of falsepositives at a sensitivity of 80% was reduced by approxi-mately a factor of 4. The improvement is a result of moredetailed 3D description of the gray-level value distributionaround the nodule candidates. Table I and Figs. 10 and 11also show that the performance in the new feature space isvery similar to that in the combined feature space. The Az

value in the new feature space �95%� is slightly better thanthat �94%� in the combined feature space. To keep the di-mensionality of the selected feature space to a minimum,26,27

it is prudent to use the 25 new features to replace the previ-ous 19 features instead of combining the two feature spaces.

In this study, we separated the data set of 91 scans into amain data set that did not contain other major diseases orsymptoms in addition to the lung nodules, and a secondarydata set that contained significant dependent atelectasis. Inthis way, we were able to analyze separately the detectionperformance for cases that contained an additional diffuseabnormality, and for cases that did not. The improvementobtained by the new feature space in our secondary data setparallels that obtained in the main data set. However, theoverall detection accuracy for the secondary data set is lowerbecause of the FPs caused by the opacities in the atelectasisareas in the CT images. The lower test Az values for this dataset compared to the main data set indicates that our featuresare not as effective in distinguishing these FPs from truenodules. We are currently investigating methods for identify-ing areas of atelectasis on CT scans so that improved tech-niques can be devised to reduce the FPs in these areas.

Based on radiologists’ ratings, 11 of the 116 nodules inour data set contained a ground-glass component. Two of the11 nodules with a ground glass component had smoothboundaries, eight had spiculated/irregular boundaries, andone had a lobulated boundary. Our prescreening algorithmdetected 111 nodules, including all 11 nodules with ground-glass component and 100 other nodules. We compared thescores attained by these two types of nodules detected by theprescreening program in our main data set. The average andstandard deviation of the scores for the 100 nodules withouta ground glass component were 4.98 and 6.67, respectively.In comparison, the corresponding numbers for the 11 noduleswith a ground-glass component were 1.40 and 5.22, respec-tively. Therefore, on average, the nodules with a ground-glass component had lower scores compared to other nod-ules. However, the difference was within one standarddeviation of the nodule scores, indicating that the differencedid not achieve statistical significance.

In this study, three thoracic radiologists with 4 to 30 yearsof experience in the interpretation of chest radiographs andthoracic CT images interpreted different subsets of the dataset. The radiologists used clinical criteria to detect nodules,to decide whether a nodule was juxta-pleural or juxta-vascular, and to provide the descriptors of nodule character-istics such as composition and margins. To minimize the in-
terobserver variability, they were provided with clear

instructions on other criteria, and with tools on a user inter-face to assist them in marking locations, making quantitativemeasurements, and recording nodule characteristics. As inother areas of diagnostic interpretation, there will be interob-server variability in these interpretations. We plan to studythe impact of interobserver variability on the performanceevaluation of the CAD system in the future by having mul-tiple radiologists to read the entire test data set. We alsoexpect that the database from the Lung Image Database Con-sortium �LIDC� will be available with gold standards pro-vided by multiple radiologists, which will serve as a bettertest set for the evaluation of our CAD system.

For all of the CT volumes in our data set, the voxel size inthe axial �x-y� plane was smaller than that in the z direction.We used linear interpolation in the z direction to interpolatethe VOI into isotropic voxels. The purpose of the interpola-tion was to facilitate the gradient calculation and other imageprocessing operations. For CT data with relatively lower spa-tial resolution in the z direction, the features of an object inthis dimension will be distorted and cannot be recovered byinterpolation. As a result of the rapid advancement in mul-tidetector row CT technology in recent years, it may be pos-sible to obtain chest CT volumes such that the z directionresolution approaches that on the x-y plane in the near future.Ellipsoid, gradient, and other shape features extracted fromdetected objects on these thinner-slice images are expected tobe more accurate and more effective for discriminating nod-ules and vessels. The performance of our FP reduction tech-nique will likely be improved when applied to CT volumeswith higher z-direction resolution.

We analyzed the types of missed lung nodules at an FPrate of 0.5/section in order to gain further insight into theperformance of our detection system. As shown in Table II,the decrease in the numbers of false-negatives for spiculated,juxta-pleural, and juxta-vascular nodules after FP reductionindicates that the new features provide better differentiationbetween these nodules and FPs than the previous featureseven for nonspherical nodules, although the new featureswere not designed specifically for these types of nodules. Itis also interesting to note that at 0.5 FPs/section, almost all ofthe missed nodules in the combined or new feature spacesare either spiculated/irregular or juxta-pleural, indicating thatthe new features are more effective for nodules with highersphericity.

Based on the main data set and a leave-one-patient-outresampling scheme, an average of 13.4 features were se-lected in the new feature space. The frequency of the featuresselected in the new feature space is tabulated in Table IV.Among the selected features, 5 are ellipsoid features, 3 aregradient field strength features, and 7 are gradient field ori-entation features. This indicates that both gradient fieldstrength and gradient field orientation features are useful forFP reduction. In addition to the ratio of the longest and short-est principal axes of the fitted ellipsoid �L13�, the lengths ofthe principal axes �L11, L22, and L33� may have been selectedby the feature selection algorithm because of their ability for
characterizing the lesion size. The remaining 10 features in


the new feature space were not selected at all, indicating thatthey were not as effective as the other features.

V. CONCLUSION

We formulated the gradient field orientation and gradientfield strength features based on the gradient field vectors atvoxels within the 3D image gradient field. Nineteen gradientfield features were derived from the statistics of these gradi-ent field vectors. In addition, six ellipsoid features were ex-tracted based on ellipsoids fitted to the binary objects. Wedemonstrated that a subset of features selected from these 3Dgradient field and 3D ellipsoid features can significantly re-duce false positives in our computerized lung nodule detec-tion system. The new 3D gradient field features and the 3Dellipsoid features can replace our previously developed fea-tures and improve the differentiation of true lung nodulesfrom other structures such as vessels. With a leave-one-patient-out training and testing scheme, the test Az valueswith the new features and with our previous features wereestimated to be 0.95±0.01 and 0.88±0.02, respectively.These classifiers reduced the FP rates to 0.37 and 1.61 persection, respectively, at 80% sensitivity for our detection sys-tem. The improvement in the test Az value with the newfeatures over that of the previous features was statisticallysignificant �two-tailed p-value�0.0001�. The features in thisstudy mainly explored the shape information using featuresaround the boundary of the identified nodule candidates. Fu-ture investigation will explore the capability of gray leveland texture information within the objects for further reduc-tion of false positive detections.

ACKNOWLEDGMENTS

This work is supported by USPHS Grant No. CA93517.The authors are thankful to Charles E. Metz, Ph.D., for pro-viding the LABROC program.

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3

TABLE IV. The frequency of the features selected in the 56 cycles of leave-one-patient-out resampling during classifier design.

Ellipsoid

Numberof timesselected

Gradient fieldorientation


Gradient fieldstrength


L11 56 GDmin 45 GMcv 55L22 35 GDcv 56 GMRstd/av 55L33 56 GD�min/max�

2 56 GMstd 56L13 35 GDav 56L23 21 GDRav 56

GDRstd 56GDstd 43

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Computer-aided detection of lung nodules: False positive